STATISTICAL PROPERTIES OF RANDOM SCATTERING MATRICES

We discuss the statistical properties of eigenphases of S matrices in random models simulating quantum systems that exhibit chaotic scatteri ng classically. The energy dependence of the eigenphases is investigat ed and the corresponding velocity and curvature distributions are obta ined both theoretically and numerically. A simple formula describing t he velocity distribution (and hence the distribution of the Wigner tim e delay) is derived that is capable of explaining the algebraic tail o f the time delay distribution observed recently in microwave experimen ts. A dependence of the eigenphases on other external parameters is al so discussed. We shaw that in the semiclassical limit (large number of channels) the curvature distribution of S-matrix eigenphases is the s ame as that corresponding to the curvature distribution of the underly ing Hamiltonian and is given by the generalized Cauchy distribution.